US9223926B2 - Method for correcting electronic proximity effects using the deconvolution of the pattern to be exposed by means of a probabilistic method - Google Patents
Method for correcting electronic proximity effects using the deconvolution of the pattern to be exposed by means of a probabilistic method Download PDFInfo
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- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/39—Circuit design at the physical level
- G06F30/398—Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM]
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
- B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
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Definitions
- the present invention applies notably to the field of electron lithography for the direct on-wafer etching or for the fabrication of masks.
- the interaction of the electron beam with the target is notably affected by a scattering of the electrons around the initial trajectory (forward scattering effect) as well as by a backscattering effect.
- These effects termed proximity effects, depend notably on the materials of the target and its geometry. It is therefore necessary to take account of the proximity effects in order to obtain etched patterns that are faithful to the defined template. Accordingly, it is known to apply two procedures, in general in an independent manner. On the one hand, the proximity effects are modeled to modulate the electron radiation doses used to bombard the target.
- the source template is modified as a function of design rules devised in a more or less empirical way so that the target template is in accordance with the objective sought.
- the reference prior art is constituted by the publication by Eisennmann (“ Proxecco—Proximity Effect Correction by Convolution” —H. Eisennmann, T. Waas, H. Hartmann—J. Vac. Sci. Technol., vol B11, N° 6, pp 2741-2745, November-December 1993) and the software marketed under the ProxeccoTM brand.
- the dose modulation is applied to a fractured pattern, each base element receiving a modulated dose which is generated with the help of a proximity effects model.
- Said model generally uses a so-called point spread function (or PSF).
- the PSF of Eisennmann is a pair of Gaussians, one for forward scattering and the other for backward scattering.
- the local doses are determined by convolving the PSF with the geometry of the target.
- the latter is if appropriate corrected according to a principle analogous to those of the Optical Proximity Correction (OPC) used in optical lithography.
- OPC Optical Proximity Correction
- the geometric correction to be applied is in general determined by automatic optimization of the dimensions of the shapes: a line will be for example thinned down, thickened, lengthened or constricted. A designer may also propose alternative geometries which are suggested to him by his know-how.
- the corrections thus determined for a type of pattern make it possible to generate correction rules which are thereafter applied automatically to all the points of the chip which have the same configuration.
- the energy radiated in a dose applied to a zone and the dimensions of the pattern to be etched on this zone are computed in combination by way of the energy latitude of the method.
- This method works well for simple patterns such as cells with large mesh size, for the ends of lines and corners, notably. It is less effective for more complex patterns.
- Another avenue for jointly optimizing the radiated dose and projected geometry parameters consists in minimizing the discrepancy between the result of convolving a radiated dose with the PSF and the target pattern. Accordingly, the suggestion has been made of deconvolving the pattern to be etched by an appropriate procedure.
- Haslam Transform based proximity corrections: Experimental results and comparisons
- the invention solves this problem by proposing to combine a PSF of a particular type with a deconvolution of the pattern to be etched using an iterative procedure of probabilistic type.
- the invention can be implemented within the framework of a method of projection lithography of cells which permits a faster rate of exposure.
- the method for correcting the proximity effects is combined by the probabilistic iterative procedure of the invention with a method for projecting cells at several levels of exposure which allows fine correction of the proximity effects.
- the invention envisages a method of lithography by radiation of at least one pattern to be irradiated on a resined support comprising at least one step of generating a chosen point spread function for said radiation and a step of applying a chosen deconvolution procedure to said pattern to be irradiated by said point spread function, said method being characterized in that said point spread function is chosen so as to model only the effects of forward scattering of said radiation and in that said deconvolution procedure is chosen from among the procedures modeling the interactions of said radiation with the resined support by a joint probability distribution of said interactions.
- said deconvolution procedure comprises a step of computing a maximum likelihood of each source point of said radiation for all the image points of the pattern to be irradiated, each image point being multiplied by the value of the point spread function between the source point and the image point.
- said deconvolution procedure is a Lucy-Richardson procedure.
- the method of lithography of the invention furthermore comprises a step of dithering the deconvolved image of the pattern to be irradiated.
- the method of lithography of the invention furthermore comprises a step of splitting the deconvolved image into at least two distinct exposure levels.
- the at least two distinct exposure levels are chosen so as to maximize the population in terms of pixels of each of the levels.
- the method of lithography of the invention furthermore comprises a step of vectorizing the deconvolved image of the pattern to be irradiated.
- the point spread function is a Gaussian.
- the mid-height width of the Gaussian is between 3 nm and 15 nm.
- a method of lithography is implemented by projection of at least one block onto a resined substrate comprising a step of decomposing said block into cells of the template to be projected onto said substrate and at least one step of forming said cells of the template by a radiating source, said method being characterized in that it furthermore comprises for at least some of the cells of the template, at least one step of extracting at least two character cells per cell of the template, each character cell being exposed in the course of a step of forming an exposure level specific to this character cell.
- the at least two character cells are chosen so as to maximize the population in terms of pixels of each of the N levels, N being equal to or greater than 2.
- these embodiments furthermore comprise a dose modulation step, said modulation applying to the N character cells.
- the invention also envisages a computer program comprising program code instructions allowing the execution of the method of lithography by radiation of the invention when the program is executed on a computer, said program comprising a function for generating a chosen point spread function for said radiation and a module for applying a chosen deconvolution procedure to the optionally filtered outputs of said radiation points spreading function applied to said pattern to be irradiated, said program being characterized in that said point spread function is chosen so as to model only the effects of forward scattering of said radiation and in that said deconvolution procedure is chosen from among the procedures modeling the interactions of the points of said radiation by a joint probability distribution of said interactions.
- the invention also envisages a computer program comprising program code instructions allowing, when the program is executed on a computer, the execution of the method of projection lithography of at least one block onto a resined substrate, said program comprising a module for decomposing said block into cells of the template to be projected onto said substrate and a module for forming said cells of the template by a radiating source, said program being characterized in that it furthermore comprises, as input of the decomposition module, a module configured to extract from at least some of the cells of the template at least two character cells per cell of the template, each character cell being exposed by an application of said forming module to an exposure level specific to this character cell.
- the computer program of the invention furthermore comprises an interface window in which an operator can programme the application to at least one second pattern belonging to a determined class of correction rules determined by deconvolution of a first pattern belonging to said class.
- the invention is particularly advantageous since it makes it possible to arrive in a completely automatic manner at an optimal radiated image.
- the limitations of the method now depend only on the limitations of the lithography machine and the arbitrations to be performed to favor the overall efficiency of the method. This level of result would not have been achievable previously, for the types of complex patterns which can thus be processed, except at the price of a dose modulation of very high precision and of very sophisticated geometric corrections requiring lengthy fine-tuning.
- the method of the invention generates a deconvolved image as gray levels which will be able to undergo different processings depending on whether a dot-matrix exposure machine or a formed-beam projection machine (of Variable Shaped Beam or VSB type) is used.
- the method of the invention makes it possible to carry out by projection of cells the irradiation of more complex patterns than the methods of the prior art, and with lower critical dimensions.
- FIG. 1 illustrates the application of modulated doses according to the prior art
- FIG. 2 represents a flowchart of the processings to be applied to implement the invention in several of its embodiments
- FIGS. 3 a and 3 b represent respectively a pattern to be exposed and its associated PSF, according to an embodiment of the invention
- FIGS. 4 a and 4 b represent respectively a gray-levels image of a pattern to be exposed and its transform into a binary image by dithering, according to an embodiment of the invention
- FIGS. 5 a and 5 b represent respectively an image in bitmap mode of a pattern to be exposed and its transform into a vector image, according to an embodiment of the invention
- FIGS. 6 a , 6 b and 6 c represent three different exposure levels, according to an embodiment of the invention.
- FIG. 7 illustrates a stencil comprising various openings for carrying out one or more irradiations in an embodiment of the invention using cell projection
- FIGS. 8 b and 8 a represent respectively a character cell of a stencil of the prior art and the cells of the template that it is sought to irradiate by a method using projection of cells corresponding to this character cell;
- FIGS. 9 a and 9 b represent respectively the two character cells determined to expose the source pattern of FIG. 8 b , according to an embodiment of the invention.
- FIGS. 10 a and 10 b represent respectively the template cell obtained after irradiation through the character cell of FIG. 8 b and that obtained after irradiation through the two character cells of FIGS. 9 a and 9 b, according to an embodiment of the invention;
- FIGS. 11 a , 11 b and 11 c represent respectively three different exposure levels carried out with three character cells according to an embodiment of the invention.
- FIG. 1 illustrates the application of modulated doses according to the prior art.
- the exposure is corrected as a function of the position of the patterns.
- the doses received are higher at the die boundary than at the center.
- the patterns situated in the interior receive in proportion backscattered electrons originating from the contiguous zones more numerous than the zones situated at the boundary.
- FIG. 2 represents a flowchart of the processings to be applied to implement the invention in several of its embodiments.
- the first steps 210 , 220 of the method of the invention are independent of the exposure tool used. It entails firstly choosing the type of PSF used. Since one is concerned essentially with the dominant phenomena on a scale of the order of some ten nanometers, it is not necessary for the backward scattering effect to be modeled in the PSF. A PSF which models only the forward scattering effect, which generates the crux of the proximity effects on the relevant scale, will therefore be chosen as a general rule in the course of step 210 .
- the PSF will be chosen to be a Gaussian whose mid-height width is between 3 nm and 15 nm. Other functions may nonetheless be appropriate, notably symmetric functions with base width of typically between 10 nm and 50 nm.
- r i ⁇ j ⁇ ⁇ u i , j ⁇ p j
- the deconvolved image is obtained as gray levels, each level at each point coding the intensity of the dose to be radiated.
- a single operation therefore makes it possible to carry out at one and the same time the dose modulation and the geometric correction, both optimal for the pattern to be exposed.
- This single operation is therefore integrated instead of these two operations into the prior art data preparation methods (dataprep) embedded in off-the-shelf electron lithography tools, with no modification other than software modification. It may however also be advantageous to optimize the computation architecture in a manner suited to the deconvolution procedure chosen.
- a suitable computation architecture will preferably be of heterogeneous nature, that is to say containing standard processors and particular computation units, for example GPUs (Graphics Processing Units, chips initially dedicated to graphics, but which today have evolved to develop unheard-of vector computation power) or FPGAs (chips whose logic circuit is programmable: it is therefore possible to programme a chip with the efficacy optimized for a given algorithm).
- GPUs Graphics Processing Units, chips initially dedicated to graphics, but which today have evolved to develop unheard-of vector computation power
- FPGAs chips whose logic circuit is programmable: it is therefore possible to programme a chip with the efficacy optimized for a given algorithm.
- step 230 a and 230 b of FIG. 2 Two main types of tool are generally used, dot-matrix tools, such as that marketed by the company Mapper and beam-forming tools, such as those marketed by the company Vistec (Vistec SB250 electron beam lithography system for example).
- dot-matrix tools such as that marketed by the company Mapper
- beam-forming tools such as those marketed by the company Vistec (Vistec SB250 electron beam lithography system for example).
- the conversion is a dithering operation.
- the second case it entails a vectorization operation.
- the exposure step 260 can then be triggered.
- FIGS. 3 a and 3 b represent respectively a pattern to be exposed and its associated PSF, according to an embodiment of the invention.
- FIG. 3 a represents a pattern to be exposed 310 a .
- Said pattern comprises complex structures, each having critical dimensions of the order of some ten nanometers.
- FIG. 3 b represents the PSF chosen 310 b .
- a PSF consisting of a Gaussian function modeling the forward scattering effect, which dominates at the dimensions of interest for structures of the types of patterns considered, is advantageously chosen.
- FIGS. 4 a and 4 b represent respectively a gray-levels image of a pattern to be exposed and its transform into a binary image by dithering, according to an embodiment of the invention.
- a tool of Mapper type accepts as input a binary image (0 or 1 pixel): the switch from gray-levels image to binary image is called dithering.
- This algorithm performs dithering by diffusing the quantization error of a pixel to its neighbors. For example, a first percentage of its error chosen as a function of the number of pixels is added to the pixel to its right, a second percentage to the pixel situated at the bottom left, a third percentage to the pixel situated below and the remainder to the pixel at the bottom right. The percentages are chosen notably as a function of the number of pixels.
- FIGS. 5 a and 5 b represent respectively an image in bitmap mode of a pattern to be exposed and its transform into a vector image, according to an embodiment of the invention.
- Vectorization is a transformation of the image as a set of points (bitmap) into a so-called vector image, which represents geometric shapes. Zones are then delimited corresponding to different doses. The gray levels of FIG. 5 a are restricted and their extent is transformed into polygons.
- vectorization algorithms are usable, for example Potrace (http://potrace.sourceforge.net/,
- FIGS. 6 a , 6 b and 6 c represent three different exposure levels, according to an embodiment of the invention.
- each level extracted by the step thus described receives a given dose which can be exposed in a single pass.
- the fine lines are eRIFs generated automatically by virtue of the invention in contradistinction to the prior art.
- a design-specific aid can be integrated into the tools at the operator's disposal.
- the geometric correction assumes an action of the operator which, as a function of his know-how and of the results of the exposures already made conceives of automatic modifications (shortening/lengthening of lines, etc.) which must be applied to all or part of the circuit.
- a tool implementing the method described can be implemented in its template application: a window, opened at his request, displays an optimal solution. The operator can then choose to generalize to patterns having the same characteristics the correction rules that he observes in this window, thus creating a library of correction rules reusable for similar patterns using for example automatic shape recognition algorithms.
- FIG. 7 illustrates a stencil comprising various openings for carrying out one or more irradiations in an embodiment of the invention using a cell projection
- FIG. 7 illustrates a stencil comprising various openings for carrying out one or more irradiations in an embodiment of the invention using a cell projection.
- a stencil 710 which is a metal plate in which “holes” are formed. These holes can be considered to be printing characters.
- Each character is a set of elementary shapes (triangles, rectangles).
- the characters are grouped together into a character cell 720 whose geometry corresponds substantially to that of the template cell to be produced (geometric corrections are nonetheless possible).
- Several character cells 720 can be produced on the same stencil to produce various template cells. As a general rule, the geometries of these character cells will differ.
- FIGS. 8 b and 8 a represent respectively a character cell of a stencil of the prior art and the cells of the template that it is sought to irradiate by a method using projection of cells corresponding to this character cell.
- the stencil of FIG. 8 b is used to irradiate the very repetitive template of FIG. 8 a .
- the single pattern 810 of FIG. 8 b replaces the hundred or so shots which would have been necessary to irradiate the same pattern by beam-formed lithography.
- the writing time when using the stencil is therefore divided accordingly.
- the precision of the irradiation is worse, notably because the backward scattering effect means that the parts of the design at the boundary of the zone 810 receive a lower dose than the parts of the design situated at the center of the zone.
- the standard cell projection lithography technique it is not possible to carry out a dose modulation within the cell of the template.
- the dose modulation is performed from one irradiation to another, i.e. from one cell of the template to another. That is to say that in practice the cell will be irradiated for a longer or shorter time depending on whether it is situated at the edge of an exposed zone or in the core. But at each exposure, the character cell will allow through the same surface dose.
- the character cell is determined after observation of the template of the circuit, so as to factorize as large a zone as possible. A geometric correction may optionally occur beforehand.
- the cell of the template 810 is split for example into two levels.
- Each level extracted by the step thus described receives a given dose which can be exposed in a single pass.
- the computation of the dose specific to each level can be performed by an extension of the dose modulation for an image to be exposed to a single level, the number N of levels constituting the number of parameters of the computation. For each exposure level, a different character cell (with different openings) is used and a specific dose is applied through each character cell.
- the correction of the effects of intra-cell proximity is carried out by applying at one and the same time a dose modulation and geometric corrections according to the method set forth above.
- the single gray-levels image output by the deconvolution is thereafter analyzed so as if appropriate to be split up into character cells intended to be exposed in several levels.
- FIGS. 10 a and 10 b represent respectively the two character cells determined to expose the source pattern of FIG. 8 b , according to an embodiment of the invention.
- the main design 910 a of FIG. 9 a is exposed on a 1 st level with a 1 st dose.
- elements 910 b are exposed on a 2 nd level with a 2 nd dose.
- the characteristic dimension of the lines and spaces of FIG. 10 a is 32 nm.
- FIG. 8 b is firstly deconvolved by a procedure of the type of those explained hereinabove as a commentary to FIGS. 8 a and 8 b.
- FIGS. 10 a and 10 b represent respectively the template cell obtained after irradiation through the character cell of FIG. 8 b and that obtained after irradiation through the two character cells of FIGS. 9 a and 9 b, according to an embodiment of the invention.
- FIG. 10 a which represents a case of the prior art, neither the widths of lines, nor the ends of lines are controlled.
- FIG. 10 b which represents the application of the invention in an embodiment with two exposure levels, the widths and the ends of lines conform to the template to be reproduced.
- FIGS. 11 a , 11 b and 11 c represent respectively three different exposure levels produced with three character cells according to an embodiment of the invention.
- FIGS. 11 a , 11 b and 11 c represent a selection of three out of ten exposure levels, said levels being determined by applying a selection procedure based on examining the brightness levels corresponding to a maximum of pixels.
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Abstract
Description
With the notation:
-
- α is the width of the direct radiation;
- β is the backscattering width;
- η is the ratio of the intensities of the direct and backscattered radiations.
- ξ is the radial position of a point (x, y).
The values of the parameters α, β and η can be determined experimentally for a given method. These parameters are dependent on the acceleration voltage of the machine and the target.
It is necessary to carry out a truncation of the high spatial frequencies to avoid the cancellation of the denominator. These frequencies being representative of the forward scattering, this is not problematic in the application described by Eisennmann.
r=F −1 [g conv ×F(p)]+C×p
Thus the part of the pattern close to the center of the beam is properly reintroduced into the resulting image, but without correction.
The algorithm therefore converges, although slowly. Other procedures from the same family, notably those termed “EM”, for Expectation—Maximization, based on an alternation of steps of computation of mathematical expectation and of likelihood maxima, will be able to be used without departing from the scope of the invention.
Claims (11)
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FR1158123 | 2011-09-13 | ||
FR1158130A FR2980001A1 (en) | 2011-09-13 | 2011-09-13 | Lithographic projection of block on resined substrate, comprises decomposition of cell block design to project on substrate, forming cell design by radiant source, and extracting two cell characters from portion of cell design |
FR1158123A FR2980000B1 (en) | 2011-09-13 | 2011-09-13 | METHOD FOR CORRECTING ELECTRONIC PROXIMITY EFFECTS USING DECONVOLUTION OF THE INSOLER PATTERN BY A PROBABILISTIC METHOD |
FR1158130 | 2011-09-13 | ||
PCT/EP2012/067756 WO2013037788A1 (en) | 2011-09-13 | 2012-09-12 | Method for correcting the effects of electronic proximity using the deconvolution of the pattern to be exposed by means of a probabilistic method |
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US11561477B2 (en) | 2017-09-08 | 2023-01-24 | Asml Netherlands B.V. | Training methods for machine learning assisted optical proximity error correction |
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NL2014314B1 (en) * | 2014-02-21 | 2016-07-19 | Mapper Lithography Ip Bv | Proximity effect correction in a charged particle lithography system. |
EP2983193B1 (en) | 2014-08-05 | 2021-10-20 | Aselta Nanographics | Method for determining the parameters of an ic manufacturing process model |
CN104537619A (en) * | 2014-12-25 | 2015-04-22 | 深圳市一体太赫兹科技有限公司 | Millimeter wave image recovery method and system |
US10674301B2 (en) | 2017-08-25 | 2020-06-02 | Google Llc | Fast and memory efficient encoding of sound objects using spherical harmonic symmetries |
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